Nullification functors and the homotopy type of the classifying space for proper bundles

Abstract

Let G be a discrete group for which the classifying space for proper G-actions is finite-dimensional. We find a space W such that for any such G, the classifying space BG for proper G-bundles has the homotopy type of the W -nullification of BG. We use this to deduce some results concerning BG and in some cases where there is a good model for BG we obtain information about the BZ/p-nullification of BG.